Canonical representations of second order stochastic processes

The representation
\begin{equation} x(t)=\sum_{n=1}^N\int_{-\infty}^tF_n(t,u)\,dz_n(u) \end{equation}
of a second order stochastic process $x(t)$, $t\in R^1$, is considered as a sum of representations for $N$ mutually orthogonal processes
\begin{equation} x_n(t)=\int_{-\infty}^tF_n(t,u)\,dz_n(u). \end{equation}
Conditions are given under which representation (1) is canonical or proper canonical (in T. Hida's terminology). These conditions are formulated in terms of the processes $x_1,\dots,x_N$ and their representations (2).